Theorems · Definition · category theory

CategoryTheory.Localization.SmallShiftedHom.shift

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {W : CategoryTheory.MorphismProperty C} →
      {M : Type w'} →
        [inst_1 : AddMonoid M] →
          [inst_2 : CategoryTheory.HasShift C M] →
            [W.IsCompatibleWithShift M] →
              {X Y : C} →
                {a : M} →
                  [inst_4 : CategoryTheory.Localization.HasSmallLocalizedShiftedHom W M X Y] →
                    [CategoryTheory.Localization.HasSmallLocalizedShiftedHom W M Y Y] →
                      CategoryTheory.Localization.SmallShiftedHom W X Y a →
                        (n a' : M) →
                          a + n = a' →
                            CategoryTheory.Localization.SmallHom W ((CategoryTheory.shiftFunctor C n).obj X)
                              ((CategoryTheory.shiftFunctor C a').obj Y)

Given f : SmallShiftedHom.{w} W X Y a, this is the element in SmallHom.{w} W (X⟦n⟧) (Y⟦a'⟧) that is obtained by shifting by n when a + n = a'.

Defined in

Mathlib.CategoryTheory.Localization.SmallShiftedHom

Cited by

4 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.MorphismProperty.IsCompatibleWithShiftCategoryTheory.Localization.HasSmallLocalizedShiftedHomCategoryTheory.Localization.HasSmallLocalizedShiftedHom